Strength-Duration Relationship in an Excitable Medium

TL;DR

This paper extends the theoretical understanding of the strength-duration relationship in one-dimensional excitable media, building on previous work that analyzed wave propagation and decay conditions, and applies it to the strength-duration curve.

Contribution

The work generalizes existing analytical criteria to include the strength-duration curve in excitable media, accommodating complex systems with moving critical solutions.

Findings

Extended the analytical framework to strength-duration curves.

Validated the theory for multicomponent and non-self-adjoint systems.

Provided criteria for wave propagation versus decay in excitable media.

Abstract

We consider the strength-duration relationship in one-dimensional spatially extended excitable media. In a previous study [Idris and Biktashev 2008] set out to separate initial (or boundary) conditions leading to propagation wave solutions from those leading to decay solutions, an analytical criterion based on an approximation of the (center-)stable manifold of a certain critical solution was presented. The theoretical prediction in the case of strength-extent curve was later on extended to cover a wider class of excitable systems including multicomponent reaction-diffusion systems, systems with non-self-adjoint linearized operators and in particular, systems with moving critical solutions (critical fronts and critical pulses) [Bezekci et al. 2015]. In the present work, we consider extension of the theory to the case of strength-duration curve.